What is 3ln(a)-2ln(b)-4ln(c) ?

The solution to 3ln(a)-2ln(b)-4ln(c) is ln((a^3)/(b^2c^4))

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simplify 3ln(a)-2ln(b)-4ln(c)

simplify

3 ln (a) - 2 ln (b) - 4 ln (c)

ln (\frac{a ^{3}}{b ^{2} c ^{4}})

Solution steps

3 ln (a) - 2 ln (b) - 4 ln (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (a) = ln (a^{3})

= ln (a^{3}) - 2 ln (b) - 4 ln (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (b) = ln (b^{2})

= ln (a^{3}) - ln (b^{2}) - 4 ln (c)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (a^{3}) - ln (b^{2}) = ln (\frac{a ^{3}}{b ^{2}})

= ln (\frac{a ^{3}}{b ^{2}}) - 4 ln (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (c) = ln (c^{4})

= ln (\frac{a ^{3}}{b ^{2}}) - ln (c^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (\frac{a ^{3}}{b ^{2}}) - ln (c^{4}) = ln (\frac{\frac{a ^{3}}{b ^{2}}}{c ^{4}})

= ln (\frac{\frac{a ^{3}}{b ^{2}}}{c ^{4}})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{a ^{3}}{b ^{2} c ^{4}})

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ln (\frac{( e - e ^{- 1} )}{2})

What is 3ln(a)-2ln(b)-4ln(c) ?
The solution to 3ln(a)-2ln(b)-4ln(c) is ln((a^3)/(b^2c^4))